Al Ferris has $$50,000$ that he wishes to invest now in order to use the accumulation for purchasing a retirement annuity in five years. After consulting with his financial advisor, he has been offered four types of fixed$-$income investments, which we will label as investments A$,$ B$,$ C$,$ and D$.$ Investments A and B are available at the beginning of each of the next five years $($call them years $1$ to $5).$ Each dollar invested in A at the beginning of a year returns $$1\mathrm{.}40($a profit of $$0\mathrm{.}40)$ two years later $($in time for immediate reinvestment$).$ Each dollar invested in B at the beginning of a year returns $$1\mathrm{.}70$ three years later. Investments C and D will each be available at one time in the future. Each dollar invested in C at the beginning of year $2$ returns $$1\mathrm{.}90$ at the end of year $5.$ Each dollar invested in D at the beginning of year $5$ returns $$1\mathrm{.}30$ at the end of year $5.$Formulate and solve a linear programming model for this problem on a spreadsheet.a$.$ Which investment plan maximizes the amount of money that can be accumulated by the beginning of year $6?$b$.$ Determine the ending balance at Year $5.$